Pair approximations, fish farms and asymmetric transmission networks

1
Pair approximations, fish farms and asymmetric
transmission networks

• ECMTB 2005
• The University of Liverpool
• Kieran Sharkey, Roger Bowers, Kenton Morgan

2
Collaboration between Liverpool University
Veterinary Epidemiology Group Liverpool
University Applied Maths Dept Lancaster
University Statistics Dept Stirling University
Institute for Aquaculture CEFAS Defra funded
Laboratory
3
Outline
The symmetric pair-wise model and FootMouth
disease
Application to fish farms
Overview of non-symmetric model
Results from non-symmetric model applied to fish
farm data
4
The Symmetric Pair-wise model
5
Contact Network
B
C
A
D
6
2001 FootMouth Outbreak
Total ban on livestock movement
Route of transmission assumes to be local
symmetric
7
S
8
S
S
t
I
9
Pair-wise Equations
dSS/dt -2?SSI dSI/dt
?(SSI-ISI-SI)-gSI dSR/dt
-?RSIgSI dII/dt 2?(ISISI)-2gII
dIR/dt ?RSIg(II-IR) dRR/dt
2gIR
10
Triples Approximation
11
Disease transmission between fish farms
Slides in this section provided by Mark Thrush at
CEFAS
12
Disease transmission matrix

• Nodes
• Fish Farms
• Fisheries
• Wild populations

• Routes of transmission
• Live fish movement
• Water flow
• Wild fish migration
• Fish farm personnel equipment

?
?
?
13
Nodes
Fish farms
14
Nodes
Fish farms
Fisheries
15
Nodes
Fish farms
Fisheries
Wild fish (EA sampling sites)
16
Thames
Test
Avon
Itchen
Stour
17
Route 1 Live Fish Movement
Thames
Test
Avon
Itchen
Stour
18
Route 2 Water flow (down stream)
19
Route 2 Water flow (down stream)
20
General pair-wise model
21
Contact network eg
0 1 1 1 0 0 0 1 0
G

22
S
I
S?I
S
I
S?I
S
I
S?I
23
-tS?S?I
-tI?S?S
24
(No Transcript)
25
(No Transcript)
26
(No Transcript)
27
(No Transcript)
28
Some results from the model
29
Nodes
Fish farms
30
3576
0
65
65
1714
65
65
8
829
0
65
0
32
8
0
0
16
0
0
0
0
0
0
0
31
Infectious Time Series
32
Infectious Time Series
33
Infectious Time Series
34
Susceptible Time Series
35
Summary
Symmetric pair-wise equations generalise to
include asymmetric transmission
Asymmetric equations perform better on
asymmetric networks.